STEPWISE TESTS WHEN THE TEST STATISTICS ARE INDEPENDENT
- 28 June 1997
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 39 (2) , 169-177
- https://doi.org/10.1111/j.1467-842x.1997.tb00533.x
Abstract
Summary: Consider the problem of simultaneously testing a nonhierarchical finite family of hypotheses based on independent test statistics. A general stepwise test is defined, of which the well known step‐down and step‐up tests are special cases. The step‐up test is shown to dominate the other stepwise tests, including the step‐down test, for situations of practical importance. When testing against two‐sided alternatives, it is pointed out that if the step‐up test is augmented to include directional decisions then the augmented step‐up test controls the type I and III familywise error jointly at the original level q. The definition of the adjusted p values for the step‐up test is justified. The results are illustrated by a numerical example.Keywords
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